ARIMA Time Series Modelling Of Excess Mortality 1975 – 2021 (summary)
England & Wales monthly excess mortality by quinary age band & sex (rev 2.1)
Autoregressive Integrated Moving Average (ARIMA) time series analysis was used to explore trends, cycles and seasonality in monthly excess mortality by quinary age group and sex for England & Wales for the period Jan 1975 – Dec 2021 as well as identify months over the period Mar 2020 - Mar 2021 with a statistically significant change in excess all cause mortality compared to the historic 5-year baseline. Initial raw statistical output along with commentary was provided in a premium content newsletter which may be found here. Time series plots (36 in total) along with data definitions and an outline of the methodology used may be found here.
Those not familiar with ARIMA time series modelling may wish to visit this Wiki entry for background on this powerful statistical technique. ARIMA model structures are defined by six parameters - ARIMA(p,d,q)(P,D,Q) -which define the order of each component:
p = non-seasonal autoregressive component - AR (lingering effects/memory)
d = non-seasonal differencing (order of underlying trend)
q = non-seasonal moving average component – MA (random signal/shocks)
P = seasonal autoregressive component - AR (lingering effects/memory)
D = seasonal differencing (order of underlying seasonal trend)
Q = seasonal moving average component – MA (random signal/shocks)
Model structure grid
In the grids below I have coloured cells to graphically represent the underlying model structure, thus the model for 0 - 4y males was ARIMA(0,1,1)(0,0,0). This may be interpreted as a simple first order trend (d=1) that is subject to random shocks arising in the previous month (q=1), there being no seasonal effects (P=0; D=0; Q=0). We may thus quickly establish which time series exhibit an underlying trend (d>0), which exhibit lingering effects (p>0) and which are subject to random shocks (q>0), along with corresponding seasonal effects (P,D,Q).
Random ‘shocks’ are to be expected since death is not an organised affair, whilst lingering effects may be thought of as runs in excess mortality. Seasonality for England & Wales is primarily driven by deteriorating respiratory conditions. Underlying trends that require differencing (d>0; D>0) to yield a stationary series will arise from a multitude of socioeconomic factors extending well beyond healthcare provision and disease.
Month Effect Grid
Binary indicator variables were established for each of the months from Mar 2020 to Mar 2021. A shaded cell indicates the indicator for the month in question reached statistical significance at the 95% level of confidence (p<0.05), with red denoting an increase and blue denoting a decrease in excess mortality. In plain English this grid reveals months where excess all cause mortality differed significantly from the 5-year historic baseline ‘normal’. Very clear patterns emerge which reveal lack of an impact of the pandemic on younger age groups and general lack of an impact of the pandemic outside the peaks of Apr 2020 and Jan 2021. There are notable exceptions worthy of further investigation and much here to contemplate!
